{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project 1: Trading with Momentum\n",
    "## Instructions\n",
    "Each problem consists of a function to implement and instructions on how to implement the function.  The parts of the function that need to be implemented are marked with a `# TODO` comment. After implementing the function, run the cell to test it against the unit tests we've provided. For each problem, we provide one or more unit tests from our `project_tests` package. These unit tests won't tell you if your answer is correct, but will warn you of any major errors. Your code will be checked for the correct solution when you submit it to Udacity.\n",
    "\n",
    "## Packages\n",
    "When you implement the functions, you'll only need to you use the packages you've used in the classroom, like [Pandas](https://pandas.pydata.org/) and [Numpy](http://www.numpy.org/). These packages will be imported for you. We recommend you don't add any import statements, otherwise the grader might not be able to run your code.\n",
    "\n",
    "The other packages that we're importing are `helper`, `project_helper`, and `project_tests`. These are custom packages built to help you solve the problems.  The `helper` and `project_helper` module contains utility functions and graph functions. The `project_tests` contains the unit tests for all the problems.\n",
    "\n",
    "### Install Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install -r requirements.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import helper\n",
    "import project_helper\n",
    "import project_tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Market Data\n",
    "\n",
    "### Download data\n",
    "For downloading data, we go to the Jupyter Notebook Workspace and after loading the date we tip:\n",
    "\n",
    "**df.to_csv('saved.csv')**\n",
    "\n",
    "We go to the file manager (File>>>>Open) and download the file to local disk in a new folder call **data** located in the same folder of this Jupyter Notebook. Finally rename the file as: **'eod-quotemedia.csv'**.\n",
    "\n",
    "### Load Data\n",
    "The data we use for most of the projects is end of day data. This contains data for many stocks, but we'll be looking at stocks in the S&P 500. We also made things a little easier to run by narrowing down our range of time period instead of using all of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded Data\n"
     ]
    }
   ],
   "source": [
    "# download the file eod-quotemedia.csv from data folder\n",
    "df = pd.read_csv('data/eod-quotemedia.csv', parse_dates=['date'], index_col=False)\n",
    "# pivot the data to obtain the date as index, the tickers in the columns and \n",
    "#the adj_close as values of the dataframe\n",
    "close = df.reset_index().pivot(index='date', columns='ticker', values='adj_close')\n",
    "\n",
    "print('Loaded Data')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>date</th>\n",
       "      <th>ticker</th>\n",
       "      <th>adj_close</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>2013-07-01</td>\n",
       "      <td>A</td>\n",
       "      <td>29.99418563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2013-07-02</td>\n",
       "      <td>A</td>\n",
       "      <td>29.65013670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2013-07-03</td>\n",
       "      <td>A</td>\n",
       "      <td>29.70518453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2013-07-05</td>\n",
       "      <td>A</td>\n",
       "      <td>30.43456826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>2013-07-08</td>\n",
       "      <td>A</td>\n",
       "      <td>30.52402098</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0       date ticker   adj_close\n",
       "0           0 2013-07-01      A 29.99418563\n",
       "1           1 2013-07-02      A 29.65013670\n",
       "2           2 2013-07-03      A 29.70518453\n",
       "3           3 2013-07-05      A 30.43456826\n",
       "4           4 2013-07-08      A 30.52402098"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 first rows of the df dataframe to review its information\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>ticker</th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABBV</th>\n",
       "      <th>ABC</th>\n",
       "      <th>ABT</th>\n",
       "      <th>ACN</th>\n",
       "      <th>ADBE</th>\n",
       "      <th>ADI</th>\n",
       "      <th>...</th>\n",
       "      <th>XL</th>\n",
       "      <th>XLNX</th>\n",
       "      <th>XOM</th>\n",
       "      <th>XRAY</th>\n",
       "      <th>XRX</th>\n",
       "      <th>XYL</th>\n",
       "      <th>YUM</th>\n",
       "      <th>ZBH</th>\n",
       "      <th>ZION</th>\n",
       "      <th>ZTS</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-07-01</th>\n",
       "      <td>29.99418563</td>\n",
       "      <td>16.17609308</td>\n",
       "      <td>81.13821681</td>\n",
       "      <td>53.10917319</td>\n",
       "      <td>34.92447839</td>\n",
       "      <td>50.86319750</td>\n",
       "      <td>31.42538772</td>\n",
       "      <td>64.69409505</td>\n",
       "      <td>46.23500000</td>\n",
       "      <td>39.91336014</td>\n",
       "      <td>...</td>\n",
       "      <td>27.66879066</td>\n",
       "      <td>35.28892781</td>\n",
       "      <td>76.32080247</td>\n",
       "      <td>40.02387348</td>\n",
       "      <td>22.10666494</td>\n",
       "      <td>25.75338607</td>\n",
       "      <td>45.48038323</td>\n",
       "      <td>71.89882693</td>\n",
       "      <td>27.85858718</td>\n",
       "      <td>29.44789315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-07-02</th>\n",
       "      <td>29.65013670</td>\n",
       "      <td>15.81983388</td>\n",
       "      <td>80.72207258</td>\n",
       "      <td>54.31224742</td>\n",
       "      <td>35.42807578</td>\n",
       "      <td>50.69676639</td>\n",
       "      <td>31.27288084</td>\n",
       "      <td>64.71204071</td>\n",
       "      <td>46.03000000</td>\n",
       "      <td>39.86057632</td>\n",
       "      <td>...</td>\n",
       "      <td>27.54228410</td>\n",
       "      <td>35.05903252</td>\n",
       "      <td>76.60816761</td>\n",
       "      <td>39.96552964</td>\n",
       "      <td>22.08273998</td>\n",
       "      <td>25.61367511</td>\n",
       "      <td>45.40266113</td>\n",
       "      <td>72.93417195</td>\n",
       "      <td>28.03893238</td>\n",
       "      <td>28.57244125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-07-03</th>\n",
       "      <td>29.70518453</td>\n",
       "      <td>16.12794994</td>\n",
       "      <td>81.23729877</td>\n",
       "      <td>54.61204262</td>\n",
       "      <td>35.44486235</td>\n",
       "      <td>50.93716689</td>\n",
       "      <td>30.72565028</td>\n",
       "      <td>65.21451912</td>\n",
       "      <td>46.42000000</td>\n",
       "      <td>40.18607651</td>\n",
       "      <td>...</td>\n",
       "      <td>27.33445191</td>\n",
       "      <td>35.28008569</td>\n",
       "      <td>76.65042719</td>\n",
       "      <td>40.00442554</td>\n",
       "      <td>22.20236479</td>\n",
       "      <td>25.73475794</td>\n",
       "      <td>46.06329899</td>\n",
       "      <td>72.30145844</td>\n",
       "      <td>28.18131017</td>\n",
       "      <td>28.16838652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-07-05</th>\n",
       "      <td>30.43456826</td>\n",
       "      <td>16.21460758</td>\n",
       "      <td>81.82188233</td>\n",
       "      <td>54.17338125</td>\n",
       "      <td>35.85613355</td>\n",
       "      <td>51.37173702</td>\n",
       "      <td>31.32670680</td>\n",
       "      <td>66.07591068</td>\n",
       "      <td>47.00000000</td>\n",
       "      <td>40.65233352</td>\n",
       "      <td>...</td>\n",
       "      <td>27.69589920</td>\n",
       "      <td>35.80177117</td>\n",
       "      <td>77.39419581</td>\n",
       "      <td>40.67537968</td>\n",
       "      <td>22.58516418</td>\n",
       "      <td>26.06075017</td>\n",
       "      <td>46.41304845</td>\n",
       "      <td>73.16424628</td>\n",
       "      <td>29.39626730</td>\n",
       "      <td>29.02459772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-07-08</th>\n",
       "      <td>30.52402098</td>\n",
       "      <td>16.31089385</td>\n",
       "      <td>82.95141667</td>\n",
       "      <td>53.86579916</td>\n",
       "      <td>36.66188936</td>\n",
       "      <td>52.03746147</td>\n",
       "      <td>31.76628544</td>\n",
       "      <td>66.82065546</td>\n",
       "      <td>46.62500000</td>\n",
       "      <td>40.25645492</td>\n",
       "      <td>...</td>\n",
       "      <td>27.98505704</td>\n",
       "      <td>35.20050655</td>\n",
       "      <td>77.96892611</td>\n",
       "      <td>40.64620776</td>\n",
       "      <td>22.48946433</td>\n",
       "      <td>26.22840332</td>\n",
       "      <td>46.95062632</td>\n",
       "      <td>73.89282298</td>\n",
       "      <td>29.57661249</td>\n",
       "      <td>29.76536472</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 495 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "ticker               A         AAL         AAP        AAPL        ABBV  \\\n",
       "date                                                                     \n",
       "2013-07-01 29.99418563 16.17609308 81.13821681 53.10917319 34.92447839   \n",
       "2013-07-02 29.65013670 15.81983388 80.72207258 54.31224742 35.42807578   \n",
       "2013-07-03 29.70518453 16.12794994 81.23729877 54.61204262 35.44486235   \n",
       "2013-07-05 30.43456826 16.21460758 81.82188233 54.17338125 35.85613355   \n",
       "2013-07-08 30.52402098 16.31089385 82.95141667 53.86579916 36.66188936   \n",
       "\n",
       "ticker             ABC         ABT         ACN        ADBE         ADI  ...  \\\n",
       "date                                                                    ...   \n",
       "2013-07-01 50.86319750 31.42538772 64.69409505 46.23500000 39.91336014  ...   \n",
       "2013-07-02 50.69676639 31.27288084 64.71204071 46.03000000 39.86057632  ...   \n",
       "2013-07-03 50.93716689 30.72565028 65.21451912 46.42000000 40.18607651  ...   \n",
       "2013-07-05 51.37173702 31.32670680 66.07591068 47.00000000 40.65233352  ...   \n",
       "2013-07-08 52.03746147 31.76628544 66.82065546 46.62500000 40.25645492  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2013-07-01 27.66879066 35.28892781 76.32080247 40.02387348 22.10666494   \n",
       "2013-07-02 27.54228410 35.05903252 76.60816761 39.96552964 22.08273998   \n",
       "2013-07-03 27.33445191 35.28008569 76.65042719 40.00442554 22.20236479   \n",
       "2013-07-05 27.69589920 35.80177117 77.39419581 40.67537968 22.58516418   \n",
       "2013-07-08 27.98505704 35.20050655 77.96892611 40.64620776 22.48946433   \n",
       "\n",
       "ticker             XYL         YUM         ZBH        ZION         ZTS  \n",
       "date                                                                    \n",
       "2013-07-01 25.75338607 45.48038323 71.89882693 27.85858718 29.44789315  \n",
       "2013-07-02 25.61367511 45.40266113 72.93417195 28.03893238 28.57244125  \n",
       "2013-07-03 25.73475794 46.06329899 72.30145844 28.18131017 28.16838652  \n",
       "2013-07-05 26.06075017 46.41304845 73.16424628 29.39626730 29.02459772  \n",
       "2013-07-08 26.22840332 46.95062632 73.89282298 29.57661249 29.76536472  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 first rows of the close dataframe to review its information\n",
    "# first date is 2013-07-01\n",
    "close.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>ticker</th>\n",
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       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
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       "      <th>...</th>\n",
       "      <th>XL</th>\n",
       "      <th>XLNX</th>\n",
       "      <th>XOM</th>\n",
       "      <th>XRAY</th>\n",
       "      <th>XRX</th>\n",
       "      <th>XYL</th>\n",
       "      <th>YUM</th>\n",
       "      <th>ZBH</th>\n",
       "      <th>ZION</th>\n",
       "      <th>ZTS</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-06-26</th>\n",
       "      <td>58.57854478</td>\n",
       "      <td>48.36234805</td>\n",
       "      <td>121.52159207</td>\n",
       "      <td>143.57270901</td>\n",
       "      <td>70.35520945</td>\n",
       "      <td>94.31043377</td>\n",
       "      <td>47.95227368</td>\n",
       "      <td>120.09101209</td>\n",
       "      <td>144.96000000</td>\n",
       "      <td>78.92677572</td>\n",
       "      <td>...</td>\n",
       "      <td>42.76892496</td>\n",
       "      <td>65.99587865</td>\n",
       "      <td>78.12543603</td>\n",
       "      <td>63.56673975</td>\n",
       "      <td>27.95461459</td>\n",
       "      <td>54.05749897</td>\n",
       "      <td>73.49934641</td>\n",
       "      <td>127.97264293</td>\n",
       "      <td>41.75554533</td>\n",
       "      <td>62.43009343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-27</th>\n",
       "      <td>58.22256443</td>\n",
       "      <td>48.08474540</td>\n",
       "      <td>121.69121741</td>\n",
       "      <td>141.51491885</td>\n",
       "      <td>70.01668424</td>\n",
       "      <td>93.85848253</td>\n",
       "      <td>47.71697322</td>\n",
       "      <td>119.94376955</td>\n",
       "      <td>142.54000000</td>\n",
       "      <td>76.54633554</td>\n",
       "      <td>...</td>\n",
       "      <td>43.14151074</td>\n",
       "      <td>63.78164638</td>\n",
       "      <td>78.00041995</td>\n",
       "      <td>63.92391201</td>\n",
       "      <td>27.75350225</td>\n",
       "      <td>53.87954816</td>\n",
       "      <td>72.74212810</td>\n",
       "      <td>127.16946735</td>\n",
       "      <td>41.95278457</td>\n",
       "      <td>62.46990854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-28</th>\n",
       "      <td>58.73675827</td>\n",
       "      <td>48.82832394</td>\n",
       "      <td>116.45278767</td>\n",
       "      <td>143.58255490</td>\n",
       "      <td>70.52930812</td>\n",
       "      <td>94.69360982</td>\n",
       "      <td>47.53069368</td>\n",
       "      <td>121.46527575</td>\n",
       "      <td>143.81000000</td>\n",
       "      <td>77.58471685</td>\n",
       "      <td>...</td>\n",
       "      <td>43.30819385</td>\n",
       "      <td>64.67321778</td>\n",
       "      <td>78.40431807</td>\n",
       "      <td>64.82428373</td>\n",
       "      <td>28.28980181</td>\n",
       "      <td>54.34419748</td>\n",
       "      <td>72.91914017</td>\n",
       "      <td>127.42727680</td>\n",
       "      <td>42.37684891</td>\n",
       "      <td>62.65903032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-29</th>\n",
       "      <td>58.27398382</td>\n",
       "      <td>49.19515602</td>\n",
       "      <td>115.79424221</td>\n",
       "      <td>141.46568942</td>\n",
       "      <td>70.10373358</td>\n",
       "      <td>94.08445815</td>\n",
       "      <td>47.77579833</td>\n",
       "      <td>120.72906307</td>\n",
       "      <td>141.24000000</td>\n",
       "      <td>76.15449354</td>\n",
       "      <td>...</td>\n",
       "      <td>43.27877918</td>\n",
       "      <td>62.88027749</td>\n",
       "      <td>77.60613845</td>\n",
       "      <td>64.10898129</td>\n",
       "      <td>28.12560699</td>\n",
       "      <td>54.27499439</td>\n",
       "      <td>72.23075989</td>\n",
       "      <td>126.81250043</td>\n",
       "      <td>43.38276899</td>\n",
       "      <td>62.21111032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-30</th>\n",
       "      <td>58.77942143</td>\n",
       "      <td>49.88916265</td>\n",
       "      <td>116.33305213</td>\n",
       "      <td>141.80044954</td>\n",
       "      <td>70.13275003</td>\n",
       "      <td>92.87597984</td>\n",
       "      <td>47.65814810</td>\n",
       "      <td>121.40637874</td>\n",
       "      <td>141.44000000</td>\n",
       "      <td>76.21326984</td>\n",
       "      <td>...</td>\n",
       "      <td>42.94541296</td>\n",
       "      <td>63.01744232</td>\n",
       "      <td>77.63498832</td>\n",
       "      <td>64.41695873</td>\n",
       "      <td>27.74892476</td>\n",
       "      <td>54.79896064</td>\n",
       "      <td>72.53561401</td>\n",
       "      <td>127.31820357</td>\n",
       "      <td>43.30387330</td>\n",
       "      <td>62.09166499</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 495 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "ticker               A         AAL          AAP         AAPL        ABBV  \\\n",
       "date                                                                       \n",
       "2017-06-26 58.57854478 48.36234805 121.52159207 143.57270901 70.35520945   \n",
       "2017-06-27 58.22256443 48.08474540 121.69121741 141.51491885 70.01668424   \n",
       "2017-06-28 58.73675827 48.82832394 116.45278767 143.58255490 70.52930812   \n",
       "2017-06-29 58.27398382 49.19515602 115.79424221 141.46568942 70.10373358   \n",
       "2017-06-30 58.77942143 49.88916265 116.33305213 141.80044954 70.13275003   \n",
       "\n",
       "ticker             ABC         ABT          ACN         ADBE         ADI  ...  \\\n",
       "date                                                                      ...   \n",
       "2017-06-26 94.31043377 47.95227368 120.09101209 144.96000000 78.92677572  ...   \n",
       "2017-06-27 93.85848253 47.71697322 119.94376955 142.54000000 76.54633554  ...   \n",
       "2017-06-28 94.69360982 47.53069368 121.46527575 143.81000000 77.58471685  ...   \n",
       "2017-06-29 94.08445815 47.77579833 120.72906307 141.24000000 76.15449354  ...   \n",
       "2017-06-30 92.87597984 47.65814810 121.40637874 141.44000000 76.21326984  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2017-06-26 42.76892496 65.99587865 78.12543603 63.56673975 27.95461459   \n",
       "2017-06-27 43.14151074 63.78164638 78.00041995 63.92391201 27.75350225   \n",
       "2017-06-28 43.30819385 64.67321778 78.40431807 64.82428373 28.28980181   \n",
       "2017-06-29 43.27877918 62.88027749 77.60613845 64.10898129 28.12560699   \n",
       "2017-06-30 42.94541296 63.01744232 77.63498832 64.41695873 27.74892476   \n",
       "\n",
       "ticker             XYL         YUM          ZBH        ZION         ZTS  \n",
       "date                                                                     \n",
       "2017-06-26 54.05749897 73.49934641 127.97264293 41.75554533 62.43009343  \n",
       "2017-06-27 53.87954816 72.74212810 127.16946735 41.95278457 62.46990854  \n",
       "2017-06-28 54.34419748 72.91914017 127.42727680 42.37684891 62.65903032  \n",
       "2017-06-29 54.27499439 72.23075989 126.81250043 43.38276899 62.21111032  \n",
       "2017-06-30 54.79896064 72.53561401 127.31820357 43.30387330 62.09166499  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 last rows of the close dataframe to review its information\n",
    "# last date is 2017-06-30\n",
    "close.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1009, 495)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# obtain the shape the close dataframe\n",
    "close.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View Data\n",
    "Run the cell below to see what the data looks like for `close`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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          "font": {
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          "line": {
           "color": "silver"
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          "values": [
           [
            "2013-07-01",
            "2013-07-02",
            "2013-07-03",
            "2013-07-05",
            "2013-07-08",
            "2013-07-09",
            "2013-07-10",
            "2013-07-11",
            "2013-07-12",
            "2013-07-15",
            "..."
           ],
           [
            "29.994",
            "29.650",
            "29.705",
            "30.435",
            "30.524",
            "30.689",
            "31.178",
            "31.460",
            "31.480",
            "31.728",
            "..."
           ],
           [
            "16.176",
            "15.820",
            "16.128",
            "16.215",
            "16.311",
            "16.715",
            "16.532",
            "16.725",
            "16.908",
            "17.100",
            "..."
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           [
            "81.138",
            "80.722",
            "81.237",
            "81.822",
            "82.951",
            "82.436",
            "81.990",
            "82.000",
            "81.911",
            "82.615",
            "..."
           ],
           [
            "...",
            "...",
            "...",
            "...",
            "...",
            "...",
            "...",
            "...",
            "...",
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            "..."
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         },
         "columnwidth": [
          1,
          3
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          "fill": {
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          "font": {
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          "values": [
           "",
           "A",
           "AAL",
           "AAP",
           "..."
          ]
         },
         "type": "table"
        }
       ],
       "layout": {}
      },
      "text/html": [
       "<div id=\"1ab78bc4-698d-4632-b179-140c99d5974b\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"1ab78bc4-698d-4632-b179-140c99d5974b\", [{\"columnwidth\": [1, 3], \"type\": \"table\", \"cells\": {\"font\": {\"size\": 13}, \"fill\": {\"color\": [\"silver\", \"white\"]}, \"line\": {\"color\": \"silver\"}, \"values\": [[\"2013-07-01\", \"2013-07-02\", \"2013-07-03\", \"2013-07-05\", \"2013-07-08\", \"2013-07-09\", \"2013-07-10\", \"2013-07-11\", \"2013-07-12\", \"2013-07-15\", \"...\"], [\"29.994\", \"29.650\", \"29.705\", \"30.435\", \"30.524\", \"30.689\", \"31.178\", \"31.460\", \"31.480\", \"31.728\", \"...\"], [\"16.176\", \"15.820\", \"16.128\", \"16.215\", \"16.311\", \"16.715\", \"16.532\", \"16.725\", \"16.908\", \"17.100\", \"...\"], [\"81.138\", \"80.722\", \"81.237\", \"81.822\", \"82.951\", \"82.436\", \"81.990\", \"82.000\", \"81.911\", \"82.615\", \"...\"], [\"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\"]]}, \"header\": {\"font\": {\"size\": 13}, \"fill\": {\"color\": \"silver\"}, \"line\": {\"color\": \"silver\"}, \"values\": [\"\", \"A\", \"AAL\", \"AAP\", \"...\"]}}], {}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"displayModeBar\": false})});</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<div id=\"1ab78bc4-698d-4632-b179-140c99d5974b\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"1ab78bc4-698d-4632-b179-140c99d5974b\", [{\"columnwidth\": [1, 3], \"type\": \"table\", \"cells\": {\"font\": {\"size\": 13}, \"fill\": {\"color\": [\"silver\", \"white\"]}, \"line\": {\"color\": \"silver\"}, \"values\": [[\"2013-07-01\", \"2013-07-02\", \"2013-07-03\", \"2013-07-05\", \"2013-07-08\", \"2013-07-09\", \"2013-07-10\", \"2013-07-11\", \"2013-07-12\", \"2013-07-15\", \"...\"], [\"29.994\", \"29.650\", \"29.705\", \"30.435\", \"30.524\", \"30.689\", \"31.178\", \"31.460\", \"31.480\", \"31.728\", \"...\"], [\"16.176\", \"15.820\", \"16.128\", \"16.215\", \"16.311\", \"16.715\", \"16.532\", \"16.725\", \"16.908\", \"17.100\", \"...\"], [\"81.138\", \"80.722\", \"81.237\", \"81.822\", \"82.951\", \"82.436\", \"81.990\", \"82.000\", \"81.911\", \"82.615\", \"...\"], [\"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\", \"...\"]]}, \"header\": {\"font\": {\"size\": 13}, \"fill\": {\"color\": \"silver\"}, \"line\": {\"color\": \"silver\"}, \"values\": [\"\", \"A\", \"AAL\", \"AAP\", \"...\"]}}], {}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"displayModeBar\": false})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "project_helper.print_dataframe(close)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stock Example\n",
    "Let's see what a single stock looks like from the closing prices. For this example and future display examples in this project, we'll use Apple's stock (AAPL). If we tried to graph all the stocks, it would be too much information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "line": {
          "color": "#2D3ECF"
         },
         "name": "Index",
         "type": "scatter",
         "x": [
          "2013-07-01",
          "2013-07-02",
          "2013-07-03",
          "2013-07-05",
          "2013-07-08",
          "2013-07-09",
          "2013-07-10",
          "2013-07-11",
          "2013-07-12",
          "2013-07-15",
          "2013-07-16",
          "2013-07-17",
          "2013-07-18",
          "2013-07-19",
          "2013-07-22",
          "2013-07-23",
          "2013-07-24",
          "2013-07-25",
          "2013-07-26",
          "2013-07-29",
          "2013-07-30",
          "2013-07-31",
          "2013-08-01",
          "2013-08-02",
          "2013-08-05",
          "2013-08-06",
          "2013-08-07",
          "2013-08-08",
          "2013-08-09",
          "2013-08-12",
          "2013-08-13",
          "2013-08-14",
          "2013-08-15",
          "2013-08-16",
          "2013-08-19",
          "2013-08-20",
          "2013-08-21",
          "2013-08-22",
          "2013-08-23",
          "2013-08-26",
          "2013-08-27",
          "2013-08-28",
          "2013-08-29",
          "2013-08-30",
          "2013-09-03",
          "2013-09-04",
          "2013-09-05",
          "2013-09-06",
          "2013-09-09",
          "2013-09-10",
          "2013-09-11",
          "2013-09-12",
          "2013-09-13",
          "2013-09-16",
          "2013-09-17",
          "2013-09-18",
          "2013-09-19",
          "2013-09-20",
          "2013-09-23",
          "2013-09-24",
          "2013-09-25",
          "2013-09-26",
          "2013-09-27",
          "2013-09-30",
          "2013-10-01",
          "2013-10-02",
          "2013-10-03",
          "2013-10-04",
          "2013-10-07",
          "2013-10-08",
          "2013-10-09",
          "2013-10-10",
          "2013-10-11",
          "2013-10-14",
          "2013-10-15",
          "2013-10-16",
          "2013-10-17",
          "2013-10-18",
          "2013-10-21",
          "2013-10-22",
          "2013-10-23",
          "2013-10-24",
          "2013-10-25",
          "2013-10-28",
          "2013-10-29",
          "2013-10-30",
          "2013-10-31",
          "2013-11-01",
          "2013-11-04",
          "2013-11-05",
          "2013-11-06",
          "2013-11-07",
          "2013-11-08",
          "2013-11-11",
          "2013-11-12",
          "2013-11-13",
          "2013-11-14",
          "2013-11-15",
          "2013-11-18",
          "2013-11-19",
          "2013-11-20",
          "2013-11-21",
          "2013-11-22",
          "2013-11-25",
          "2013-11-26",
          "2013-11-27",
          "2013-11-29",
          "2013-12-02",
          "2013-12-03",
          "2013-12-04",
          "2013-12-05",
          "2013-12-06",
          "2013-12-09",
          "2013-12-10",
          "2013-12-11",
          "2013-12-12",
          "2013-12-13",
          "2013-12-16",
          "2013-12-17",
          "2013-12-18",
          "2013-12-19",
          "2013-12-20",
          "2013-12-23",
          "2013-12-24",
          "2013-12-26",
          "2013-12-27",
          "2013-12-30",
          "2013-12-31",
          "2014-01-02",
          "2014-01-03",
          "2014-01-06",
          "2014-01-07",
          "2014-01-08",
          "2014-01-09",
          "2014-01-10",
          "2014-01-13",
          "2014-01-14",
          "2014-01-15",
          "2014-01-16",
          "2014-01-17",
          "2014-01-21",
          "2014-01-22",
          "2014-01-23",
          "2014-01-24",
          "2014-01-27",
          "2014-01-28",
          "2014-01-29",
          "2014-01-30",
          "2014-01-31",
          "2014-02-03",
          "2014-02-04",
          "2014-02-05",
          "2014-02-06",
          "2014-02-07",
          "2014-02-10",
          "2014-02-11",
          "2014-02-12",
          "2014-02-13",
          "2014-02-14",
          "2014-02-18",
          "2014-02-19",
          "2014-02-20",
          "2014-02-21",
          "2014-02-24",
          "2014-02-25",
          "2014-02-26",
          "2014-02-27",
          "2014-02-28",
          "2014-03-03",
          "2014-03-04",
          "2014-03-05",
          "2014-03-06",
          "2014-03-07",
          "2014-03-10",
          "2014-03-11",
          "2014-03-12",
          "2014-03-13",
          "2014-03-14",
          "2014-03-17",
          "2014-03-18",
          "2014-03-19",
          "2014-03-20",
          "2014-03-21",
          "2014-03-24",
          "2014-03-25",
          "2014-03-26",
          "2014-03-27",
          "2014-03-28",
          "2014-03-31",
          "2014-04-01",
          "2014-04-02",
          "2014-04-03",
          "2014-04-04",
          "2014-04-07",
          "2014-04-08",
          "2014-04-09",
          "2014-04-10",
          "2014-04-11",
          "2014-04-14",
          "2014-04-15",
          "2014-04-16",
          "2014-04-17",
          "2014-04-21",
          "2014-04-22",
          "2014-04-23",
          "2014-04-24",
          "2014-04-25",
          "2014-04-28",
          "2014-04-29",
          "2014-04-30",
          "2014-05-01",
          "2014-05-02",
          "2014-05-05",
          "2014-05-06",
          "2014-05-07",
          "2014-05-08",
          "2014-05-09",
          "2014-05-12",
          "2014-05-13",
          "2014-05-14",
          "2014-05-15",
          "2014-05-16",
          "2014-05-19",
          "2014-05-20",
          "2014-05-21",
          "2014-05-22",
          "2014-05-23",
          "2014-05-27",
          "2014-05-28",
          "2014-05-29",
          "2014-05-30",
          "2014-06-02",
          "2014-06-03",
          "2014-06-04",
          "2014-06-05",
          "2014-06-06",
          "2014-06-09",
          "2014-06-10",
          "2014-06-11",
          "2014-06-12",
          "2014-06-13",
          "2014-06-16",
          "2014-06-17",
          "2014-06-18",
          "2014-06-19",
          "2014-06-20",
          "2014-06-23",
          "2014-06-24",
          "2014-06-25",
          "2014-06-26",
          "2014-06-27",
          "2014-06-30",
          "2014-07-01",
          "2014-07-02",
          "2014-07-03",
          "2014-07-07",
          "2014-07-08",
          "2014-07-09",
          "2014-07-10",
          "2014-07-11",
          "2014-07-14",
          "2014-07-15",
          "2014-07-16",
          "2014-07-17",
          "2014-07-18",
          "2014-07-21",
          "2014-07-22",
          "2014-07-23",
          "2014-07-24",
          "2014-07-25",
          "2014-07-28",
          "2014-07-29",
          "2014-07-30",
          "2014-07-31",
          "2014-08-01",
          "2014-08-04",
          "2014-08-05",
          "2014-08-06",
          "2014-08-07",
          "2014-08-08",
          "2014-08-11",
          "2014-08-12",
          "2014-08-13",
          "2014-08-14",
          "2014-08-15",
          "2014-08-18",
          "2014-08-19",
          "2014-08-20",
          "2014-08-21",
          "2014-08-22",
          "2014-08-25",
          "2014-08-26",
          "2014-08-27",
          "2014-08-28",
          "2014-08-29",
          "2014-09-02",
          "2014-09-03",
          "2014-09-04",
          "2014-09-05",
          "2014-09-08",
          "2014-09-09",
          "2014-09-10",
          "2014-09-11",
          "2014-09-12",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "apple_ticker = 'AAPL'\n",
    "project_helper.plot_stock(close[apple_ticker], '{} Stock'.format(apple_ticker))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resample Adjusted Prices\n",
    "\n",
    "The trading signal you'll develop in this project does not need to be based on daily prices, for instance, you can use month-end prices to perform trading once a month. To do this, you must first resample the daily adjusted closing prices into monthly buckets, and select the last observation of each month.\n",
    "\n",
    "Implement the `resample_prices` to resample `close_prices` at the sampling frequency of `freq`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tests Passed\n"
     ]
    }
   ],
   "source": [
    "def resample_prices(close_prices, freq='M'):\n",
    "    \"\"\"\n",
    "    Resample close prices for each ticker at specified frequency.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    close_prices : DataFrame\n",
    "        Close prices for each ticker and date\n",
    "    freq : str\n",
    "        What frequency to sample at\n",
    "        For valid freq choices, see http://pandas.pydata.org/pandas-docs/stable/timeseries.html#offset-aliases\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    prices_resampled : DataFrame\n",
    "        Resampled prices for each ticker and date\n",
    "    \"\"\"\n",
    "    # TODO: Implement Function\n",
    "    # resample the close prices for a sampling frequency of freq\n",
    "    # in this case, last day of eeach month\n",
    "    close_prices_monthly = close_prices.resample(freq).last()\n",
    "    # return the dataframe resampled\n",
    "    return close_prices_monthly\n",
    "\n",
    "project_tests.test_resample_prices(resample_prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View Data\n",
    "Let's apply this function to `close` and view the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "line": {
          "color": "#2D3ECF"
         },
         "mode": "line",
         "name": "Monthly Close",
         "type": "scatter",
         "x": [
          "2013-07-31",
          "2013-08-31",
          "2013-09-30",
          "2013-10-31",
          "2013-11-30",
          "2013-12-31",
          "2014-01-31",
          "2014-02-28",
          "2014-03-31",
          "2014-04-30",
          "2014-05-31",
          "2014-06-30",
          "2014-07-31",
          "2014-08-31",
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\"2017-06-08\", \"2017-06-09\", \"2017-06-12\", \"2017-06-13\", \"2017-06-14\", \"2017-06-15\", \"2017-06-16\", \"2017-06-19\", \"2017-06-20\", \"2017-06-21\", \"2017-06-22\", \"2017-06-23\", \"2017-06-26\", \"2017-06-27\", \"2017-06-28\", \"2017-06-29\", \"2017-06-30\"]}], {\"title\": \"AAPL Stock - Close Vs Monthly Close\"}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"displayModeBar\": false})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "monthly_close = resample_prices(close)\n",
    "project_helper.plot_resampled_prices(\n",
    "    monthly_close.loc[:, apple_ticker],\n",
    "    close.loc[:, apple_ticker],\n",
    "    '{} Stock - Close Vs Monthly Close'.format(apple_ticker))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48, 495)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# obtain the shape the monthly_close dataframe\n",
    "monthly_close.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>24.75516170</td>\n",
       "      <td>26.13637721</td>\n",
       "      <td>46.45223934</td>\n",
       "      <td>78.93635707</td>\n",
       "      <td>26.06190225</td>\n",
       "      <td>30.00331147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-31</th>\n",
       "      <td>35.00902763</td>\n",
       "      <td>21.15409315</td>\n",
       "      <td>98.34285959</td>\n",
       "      <td>68.28583759</td>\n",
       "      <td>41.39637606</td>\n",
       "      <td>60.85069550</td>\n",
       "      <td>33.05576095</td>\n",
       "      <td>66.82299697</td>\n",
       "      <td>54.22000000</td>\n",
       "      <td>43.69008561</td>\n",
       "      <td>...</td>\n",
       "      <td>27.75007493</td>\n",
       "      <td>40.38659157</td>\n",
       "      <td>76.27208656</td>\n",
       "      <td>45.87069305</td>\n",
       "      <td>23.91314940</td>\n",
       "      <td>32.41710942</td>\n",
       "      <td>44.24404652</td>\n",
       "      <td>84.05847719</td>\n",
       "      <td>26.98861102</td>\n",
       "      <td>30.58582019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-30</th>\n",
       "      <td>36.94707663</td>\n",
       "      <td>22.60801580</td>\n",
       "      <td>100.15741326</td>\n",
       "      <td>73.07037475</td>\n",
       "      <td>41.39637606</td>\n",
       "      <td>65.91719111</td>\n",
       "      <td>34.53897430</td>\n",
       "      <td>70.43234797</td>\n",
       "      <td>56.78000000</td>\n",
       "      <td>42.73298029</td>\n",
       "      <td>...</td>\n",
       "      <td>29.03908724</td>\n",
       "      <td>39.71607441</td>\n",
       "      <td>80.10221273</td>\n",
       "      <td>46.31377055</td>\n",
       "      <td>27.37742858</td>\n",
       "      <td>32.47348700</td>\n",
       "      <td>50.82634626</td>\n",
       "      <td>87.84481134</td>\n",
       "      <td>27.91674534</td>\n",
       "      <td>30.09312378</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 495 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "ticker               A         AAL          AAP        AAPL        ABBV  \\\n",
       "date                                                                      \n",
       "2013-07-31 30.77861719 18.63139292  81.73270857 58.73000866 38.52144972   \n",
       "2013-08-31 32.09288410 15.55986096  79.33492514 63.64994327 36.09056668   \n",
       "2013-09-30 35.34697923 18.25587647  81.98212977 62.28266407 37.88620154   \n",
       "2013-10-31 35.00902763 21.15409315  98.34285959 68.28583759 41.39637606   \n",
       "2013-11-30 36.94707663 22.60801580 100.15741326 73.07037475 41.39637606   \n",
       "\n",
       "ticker             ABC         ABT         ACN        ADBE         ADI  ...  \\\n",
       "date                                                                    ...   \n",
       "2013-07-31 53.87744989 32.99081455 66.22844876 47.28000000 43.44107832  ...   \n",
       "2013-08-31 53.01732111 30.01866909 64.82868748 45.75000000 41.01373554  ...   \n",
       "2013-09-30 56.91072241 29.89257807 66.07591068 51.94000000 41.69611619  ...   \n",
       "2013-10-31 60.85069550 33.05576095 66.82299697 54.22000000 43.69008561  ...   \n",
       "2013-11-30 65.91719111 34.53897430 70.43234797 56.78000000 42.73298029  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2013-07-31 28.32843198 41.28388974 79.23671352 41.69639686 23.20721320   \n",
       "2013-08-31 26.71095532 38.60058125 74.17847651 40.83096325 23.87711213   \n",
       "2013-09-30 27.97701372 41.65075616 73.22528819 42.27738327 24.75516170   \n",
       "2013-10-31 27.75007493 40.38659157 76.27208656 45.87069305 23.91314940   \n",
       "2013-11-30 29.03908724 39.71607441 80.10221273 46.31377055 27.37742858   \n",
       "\n",
       "ticker             XYL         YUM         ZBH        ZION         ZTS  \n",
       "date                                                                    \n",
       "2013-07-31 23.21996075 47.44778390 80.02819050 28.13385091 28.74031861  \n",
       "2013-08-31 23.18866549 45.56080402 75.81970579 26.58466104 28.10400159  \n",
       "2013-09-30 26.13637721 46.45223934 78.93635707 26.06190225 30.00331147  \n",
       "2013-10-31 32.41710942 44.24404652 84.05847719 26.98861102 30.58582019  \n",
       "2013-11-30 32.47348700 50.82634626 87.84481134 27.91674534 30.09312378  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 first rows of the monthly close dataframe to review its information\n",
    "# first date is 2013-07-31\n",
    "monthly_close.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>ticker</th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABBV</th>\n",
       "      <th>ABC</th>\n",
       "      <th>ABT</th>\n",
       "      <th>ACN</th>\n",
       "      <th>ADBE</th>\n",
       "      <th>ADI</th>\n",
       "      <th>...</th>\n",
       "      <th>XL</th>\n",
       "      <th>XLNX</th>\n",
       "      <th>XOM</th>\n",
       "      <th>XRAY</th>\n",
       "      <th>XRX</th>\n",
       "      <th>XYL</th>\n",
       "      <th>YUM</th>\n",
       "      <th>ZBH</th>\n",
       "      <th>ZION</th>\n",
       "      <th>ZTS</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-02-28</th>\n",
       "      <td>50.60086565</td>\n",
       "      <td>45.86299598</td>\n",
       "      <td>156.12490616</td>\n",
       "      <td>134.32908516</td>\n",
       "      <td>59.22200826</td>\n",
       "      <td>89.53185633</td>\n",
       "      <td>43.93014132</td>\n",
       "      <td>119.00755442</td>\n",
       "      <td>118.34000000</td>\n",
       "      <td>79.81469100</td>\n",
       "      <td>...</td>\n",
       "      <td>39.27808058</td>\n",
       "      <td>57.31683497</td>\n",
       "      <td>77.47406925</td>\n",
       "      <td>62.93356886</td>\n",
       "      <td>28.25756141</td>\n",
       "      <td>47.41055399</td>\n",
       "      <td>63.93671203</td>\n",
       "      <td>115.64850010</td>\n",
       "      <td>44.19325569</td>\n",
       "      <td>52.86838150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-03-31</th>\n",
       "      <td>52.27967020</td>\n",
       "      <td>41.84652135</td>\n",
       "      <td>147.85939394</td>\n",
       "      <td>140.86952606</td>\n",
       "      <td>62.40145631</td>\n",
       "      <td>86.58692258</td>\n",
       "      <td>43.27723105</td>\n",
       "      <td>116.46224999</td>\n",
       "      <td>130.13000000</td>\n",
       "      <td>79.83417463</td>\n",
       "      <td>...</td>\n",
       "      <td>38.88040598</td>\n",
       "      <td>56.41060144</td>\n",
       "      <td>78.13143654</td>\n",
       "      <td>61.94954316</td>\n",
       "      <td>28.11741981</td>\n",
       "      <td>49.47959312</td>\n",
       "      <td>62.54678351</td>\n",
       "      <td>120.85551089</td>\n",
       "      <td>41.33890287</td>\n",
       "      <td>52.92788446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-04-30</th>\n",
       "      <td>54.43532901</td>\n",
       "      <td>42.16309078</td>\n",
       "      <td>141.75593049</td>\n",
       "      <td>140.85972030</td>\n",
       "      <td>63.77814835</td>\n",
       "      <td>80.27635025</td>\n",
       "      <td>42.78546766</td>\n",
       "      <td>119.07013051</td>\n",
       "      <td>133.74000000</td>\n",
       "      <td>74.23263096</td>\n",
       "      <td>...</td>\n",
       "      <td>40.82150000</td>\n",
       "      <td>61.49720257</td>\n",
       "      <td>77.78846230</td>\n",
       "      <td>62.74325928</td>\n",
       "      <td>27.54281314</td>\n",
       "      <td>50.65204864</td>\n",
       "      <td>64.65857676</td>\n",
       "      <td>118.42078354</td>\n",
       "      <td>39.39991148</td>\n",
       "      <td>55.75615969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-31</th>\n",
       "      <td>59.66626253</td>\n",
       "      <td>47.99551598</td>\n",
       "      <td>133.26892494</td>\n",
       "      <td>150.40575387</td>\n",
       "      <td>63.85552554</td>\n",
       "      <td>90.16427240</td>\n",
       "      <td>44.76591323</td>\n",
       "      <td>122.18185609</td>\n",
       "      <td>141.86000000</td>\n",
       "      <td>83.54580618</td>\n",
       "      <td>...</td>\n",
       "      <td>42.61628041</td>\n",
       "      <td>65.35904193</td>\n",
       "      <td>77.41380602</td>\n",
       "      <td>63.02105992</td>\n",
       "      <td>27.08312780</td>\n",
       "      <td>51.54641544</td>\n",
       "      <td>71.43420556</td>\n",
       "      <td>117.98530385</td>\n",
       "      <td>39.51688006</td>\n",
       "      <td>61.88725050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-30</th>\n",
       "      <td>58.77942143</td>\n",
       "      <td>49.88916265</td>\n",
       "      <td>116.33305213</td>\n",
       "      <td>141.80044954</td>\n",
       "      <td>70.13275003</td>\n",
       "      <td>92.87597984</td>\n",
       "      <td>47.65814810</td>\n",
       "      <td>121.40637874</td>\n",
       "      <td>141.44000000</td>\n",
       "      <td>76.21326984</td>\n",
       "      <td>...</td>\n",
       "      <td>42.94541296</td>\n",
       "      <td>63.01744232</td>\n",
       "      <td>77.63498832</td>\n",
       "      <td>64.41695873</td>\n",
       "      <td>27.74892476</td>\n",
       "      <td>54.79896064</td>\n",
       "      <td>72.53561401</td>\n",
       "      <td>127.31820357</td>\n",
       "      <td>43.30387330</td>\n",
       "      <td>62.09166499</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 495 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "ticker               A         AAL          AAP         AAPL        ABBV  \\\n",
       "date                                                                       \n",
       "2017-02-28 50.60086565 45.86299598 156.12490616 134.32908516 59.22200826   \n",
       "2017-03-31 52.27967020 41.84652135 147.85939394 140.86952606 62.40145631   \n",
       "2017-04-30 54.43532901 42.16309078 141.75593049 140.85972030 63.77814835   \n",
       "2017-05-31 59.66626253 47.99551598 133.26892494 150.40575387 63.85552554   \n",
       "2017-06-30 58.77942143 49.88916265 116.33305213 141.80044954 70.13275003   \n",
       "\n",
       "ticker             ABC         ABT          ACN         ADBE         ADI  ...  \\\n",
       "date                                                                      ...   \n",
       "2017-02-28 89.53185633 43.93014132 119.00755442 118.34000000 79.81469100  ...   \n",
       "2017-03-31 86.58692258 43.27723105 116.46224999 130.13000000 79.83417463  ...   \n",
       "2017-04-30 80.27635025 42.78546766 119.07013051 133.74000000 74.23263096  ...   \n",
       "2017-05-31 90.16427240 44.76591323 122.18185609 141.86000000 83.54580618  ...   \n",
       "2017-06-30 92.87597984 47.65814810 121.40637874 141.44000000 76.21326984  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2017-02-28 39.27808058 57.31683497 77.47406925 62.93356886 28.25756141   \n",
       "2017-03-31 38.88040598 56.41060144 78.13143654 61.94954316 28.11741981   \n",
       "2017-04-30 40.82150000 61.49720257 77.78846230 62.74325928 27.54281314   \n",
       "2017-05-31 42.61628041 65.35904193 77.41380602 63.02105992 27.08312780   \n",
       "2017-06-30 42.94541296 63.01744232 77.63498832 64.41695873 27.74892476   \n",
       "\n",
       "ticker             XYL         YUM          ZBH        ZION         ZTS  \n",
       "date                                                                     \n",
       "2017-02-28 47.41055399 63.93671203 115.64850010 44.19325569 52.86838150  \n",
       "2017-03-31 49.47959312 62.54678351 120.85551089 41.33890287 52.92788446  \n",
       "2017-04-30 50.65204864 64.65857676 118.42078354 39.39991148 55.75615969  \n",
       "2017-05-31 51.54641544 71.43420556 117.98530385 39.51688006 61.88725050  \n",
       "2017-06-30 54.79896064 72.53561401 127.31820357 43.30387330 62.09166499  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 last rows of the monthly close dataframe to review its information\n",
    "# last date is 2017-06-30\n",
    "monthly_close.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Log Returns\n",
    "\n",
    "Compute log returns ($R_t$) from prices ($P_t$) as your primary momentum indicator:\n",
    "\n",
    "$$R_t = log_e(P_t) - log_e(P_{t-1})$$\n",
    "\n",
    "Implement the `compute_log_returns` function below, such that it accepts a dataframe (like one returned by `resample_prices`), and produces a similar dataframe of log returns. Use Numpy's [log function](https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html) to help you calculate the log returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tests Passed\n"
     ]
    }
   ],
   "source": [
    "def compute_log_returns(prices):\n",
    "    \"\"\"\n",
    "    Compute log returns for each ticker.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    prices : DataFrame\n",
    "        Prices for each ticker and date\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    log_returns : DataFrame\n",
    "        Log returns for each ticker and date\n",
    "    \"\"\"\n",
    "    # TODO: Implement Function\n",
    "    # compute log returns as ln(p_t) - ln(p_t-1)\n",
    "    # shift() function, moves data prices in a given time\n",
    "    log_stock_returns = np.log(prices) - np.log(prices.shift(1))\n",
    "    # return log_stock_returns\n",
    "    return log_stock_returns\n",
    "\n",
    "project_tests.test_compute_log_returns(compute_log_returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View Data\n",
    "Using the same data returned from `resample_prices`, we'll generate the log returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "line": {
          "color": "#2D3ECF"
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         "mode": "line",
         "name": "Returns",
         "type": "scatter",
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       "layout": {
        "title": "Log Returns of AAPL Stock (Monthly)"
       }
      },
      "text/html": [
       "<div id=\"ce4ca4a1-65b4-4f49-91bb-77f687c143bd\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"ce4ca4a1-65b4-4f49-91bb-77f687c143bd\", [{\"type\": \"scatter\", \"line\": {\"color\": \"#2D3ECF\"}, \"mode\": \"line\", \"y\": [null, 0.0804476167699244, -0.02171531209840971, 0.09201926751761658, 0.06772062528255329, 0.008862369904605316, -0.11394917651344016, 0.05588346896232643, 0.0197564234971761, 0.09476126170131938, 0.07577509203027688, 0.027286248480385744, 0.02832629848810697, 0.0746522438902959, -0.017220597751671285, 0.06948902629742815, 0.10071836377994803, -0.0746061267277982, 0.05961156394817735, 0.09598801803387769, -0.0318742630421065, 0.005769709090243325, 0.04431573454833959, -0.03797801003771628, -0.033441154420311925, -0.06849868571221762, -0.025235949245141498, 0.08329065437079475, -0.005801456651161274, -0.11679029105870864, -0.07822347552032394, -0.001331433817136407, 0.11974615040576353, -0.1507311424066602, 0.06933885854820687, -0.04359638501510865, 0.08623527394698094, 0.023343471369801527, 0.06344815310404162, 0.004324999018601616, -0.021782279644624758, 0.046840761742427794, 0.04664167037496725, 0.12552424621905978, 0.04754146618335664, -6.961122135695774e-05, 0.06557216424023249, -0.05891588353659394], \"name\": \"Returns\", \"x\": [\"2013-07-31\", \"2013-08-31\", \"2013-09-30\", \"2013-10-31\", \"2013-11-30\", \"2013-12-31\", \"2014-01-31\", \"2014-02-28\", \"2014-03-31\", \"2014-04-30\", \"2014-05-31\", \"2014-06-30\", \"2014-07-31\", \"2014-08-31\", \"2014-09-30\", \"2014-10-31\", \"2014-11-30\", \"2014-12-31\", \"2015-01-31\", \"2015-02-28\", \"2015-03-31\", \"2015-04-30\", \"2015-05-31\", \"2015-06-30\", \"2015-07-31\", \"2015-08-31\", \"2015-09-30\", \"2015-10-31\", \"2015-11-30\", \"2015-12-31\", \"2016-01-31\", \"2016-02-29\", \"2016-03-31\", \"2016-04-30\", \"2016-05-31\", \"2016-06-30\", \"2016-07-31\", \"2016-08-31\", \"2016-09-30\", \"2016-10-31\", \"2016-11-30\", \"2016-12-31\", \"2017-01-31\", \"2017-02-28\", \"2017-03-31\", \"2017-04-30\", \"2017-05-31\", \"2017-06-30\"]}], {\"title\": \"Log Returns of AAPL Stock (Monthly)\"}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"displayModeBar\": false})});</script>"
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      "text/vnd.plotly.v1+html": [
       "<div id=\"ce4ca4a1-65b4-4f49-91bb-77f687c143bd\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"ce4ca4a1-65b4-4f49-91bb-77f687c143bd\", [{\"type\": \"scatter\", \"line\": {\"color\": \"#2D3ECF\"}, \"mode\": \"line\", \"y\": [null, 0.0804476167699244, -0.02171531209840971, 0.09201926751761658, 0.06772062528255329, 0.008862369904605316, -0.11394917651344016, 0.05588346896232643, 0.0197564234971761, 0.09476126170131938, 0.07577509203027688, 0.027286248480385744, 0.02832629848810697, 0.0746522438902959, -0.017220597751671285, 0.06948902629742815, 0.10071836377994803, -0.0746061267277982, 0.05961156394817735, 0.09598801803387769, -0.0318742630421065, 0.005769709090243325, 0.04431573454833959, -0.03797801003771628, -0.033441154420311925, -0.06849868571221762, -0.025235949245141498, 0.08329065437079475, -0.005801456651161274, -0.11679029105870864, -0.07822347552032394, -0.001331433817136407, 0.11974615040576353, -0.1507311424066602, 0.06933885854820687, -0.04359638501510865, 0.08623527394698094, 0.023343471369801527, 0.06344815310404162, 0.004324999018601616, -0.021782279644624758, 0.046840761742427794, 0.04664167037496725, 0.12552424621905978, 0.04754146618335664, -6.961122135695774e-05, 0.06557216424023249, -0.05891588353659394], \"name\": \"Returns\", \"x\": [\"2013-07-31\", \"2013-08-31\", \"2013-09-30\", \"2013-10-31\", \"2013-11-30\", \"2013-12-31\", \"2014-01-31\", \"2014-02-28\", \"2014-03-31\", \"2014-04-30\", \"2014-05-31\", \"2014-06-30\", \"2014-07-31\", \"2014-08-31\", \"2014-09-30\", \"2014-10-31\", \"2014-11-30\", \"2014-12-31\", \"2015-01-31\", \"2015-02-28\", \"2015-03-31\", \"2015-04-30\", \"2015-05-31\", \"2015-06-30\", \"2015-07-31\", \"2015-08-31\", \"2015-09-30\", \"2015-10-31\", \"2015-11-30\", \"2015-12-31\", \"2016-01-31\", \"2016-02-29\", \"2016-03-31\", \"2016-04-30\", \"2016-05-31\", \"2016-06-30\", \"2016-07-31\", \"2016-08-31\", \"2016-09-30\", \"2016-10-31\", \"2016-11-30\", \"2016-12-31\", \"2017-01-31\", \"2017-02-28\", \"2017-03-31\", \"2017-04-30\", \"2017-05-31\", \"2017-06-30\"]}], {\"title\": \"Log Returns of AAPL Stock (Monthly)\"}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"displayModeBar\": false})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "monthly_close_returns = compute_log_returns(monthly_close)\n",
    "project_helper.plot_returns(\n",
    "    monthly_close_returns.loc[:, apple_ticker],\n",
    "    'Log Returns of {} Stock (Monthly)'.format(apple_ticker))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48, 495)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# obtain the shape the monthly_close_returns dataframe\n",
    "monthly_close_returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>ticker</th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABBV</th>\n",
       "      <th>ABC</th>\n",
       "      <th>ABT</th>\n",
       "      <th>ACN</th>\n",
       "      <th>ADBE</th>\n",
       "      <th>ADI</th>\n",
       "      <th>...</th>\n",
       "      <th>XL</th>\n",
       "      <th>XLNX</th>\n",
       "      <th>XOM</th>\n",
       "      <th>XRAY</th>\n",
       "      <th>XRX</th>\n",
       "      <th>XYL</th>\n",
       "      <th>YUM</th>\n",
       "      <th>ZBH</th>\n",
       "      <th>ZION</th>\n",
       "      <th>ZTS</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-07-31</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
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       "      <td>...</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
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       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
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       "    <tr>\n",
       "      <th>2013-08-31</th>\n",
       "      <td>0.04181412</td>\n",
       "      <td>-0.18015337</td>\n",
       "      <td>-0.02977582</td>\n",
       "      <td>0.08044762</td>\n",
       "      <td>-0.06518370</td>\n",
       "      <td>-0.01609335</td>\n",
       "      <td>-0.09440968</td>\n",
       "      <td>-0.02136190</td>\n",
       "      <td>-0.03289558</td>\n",
       "      <td>-0.05749847</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.05879217</td>\n",
       "      <td>-0.06720501</td>\n",
       "      <td>-0.06596571</td>\n",
       "      <td>-0.02097402</td>\n",
       "      <td>0.02845720</td>\n",
       "      <td>-0.00134868</td>\n",
       "      <td>-0.04058203</td>\n",
       "      <td>-0.05402072</td>\n",
       "      <td>-0.05663911</td>\n",
       "      <td>-0.02238899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-09-30</th>\n",
       "      <td>0.09657861</td>\n",
       "      <td>0.15979244</td>\n",
       "      <td>0.03282284</td>\n",
       "      <td>-0.02171531</td>\n",
       "      <td>0.04855545</td>\n",
       "      <td>0.07086509</td>\n",
       "      <td>-0.00420927</td>\n",
       "      <td>0.01905603</td>\n",
       "      <td>0.12689741</td>\n",
       "      <td>0.01650096</td>\n",
       "      <td>...</td>\n",
       "      <td>0.04630944</td>\n",
       "      <td>0.07605219</td>\n",
       "      <td>-0.01293321</td>\n",
       "      <td>0.03481157</td>\n",
       "      <td>0.03611367</td>\n",
       "      <td>0.11966450</td>\n",
       "      <td>0.01937689</td>\n",
       "      <td>0.04028369</td>\n",
       "      <td>-0.01985983</td>\n",
       "      <td>0.06539579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-31</th>\n",
       "      <td>-0.00960698</td>\n",
       "      <td>0.14734639</td>\n",
       "      <td>0.18195865</td>\n",
       "      <td>0.09201927</td>\n",
       "      <td>0.08860637</td>\n",
       "      <td>0.06693948</td>\n",
       "      <td>0.10058564</td>\n",
       "      <td>0.01124304</td>\n",
       "      <td>0.04296064</td>\n",
       "      <td>0.04671322</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.00814469</td>\n",
       "      <td>-0.03082169</td>\n",
       "      <td>0.04076620</td>\n",
       "      <td>0.08157415</td>\n",
       "      <td>-0.03460553</td>\n",
       "      <td>0.21535825</td>\n",
       "      <td>-0.04870385</td>\n",
       "      <td>0.06287079</td>\n",
       "      <td>0.03494040</td>\n",
       "      <td>0.01922875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-30</th>\n",
       "      <td>0.05388057</td>\n",
       "      <td>0.06647111</td>\n",
       "      <td>0.01828314</td>\n",
       "      <td>0.06772063</td>\n",
       "      <td>0.00000000</td>\n",
       "      <td>0.07997603</td>\n",
       "      <td>0.04389252</td>\n",
       "      <td>0.05260536</td>\n",
       "      <td>0.04613431</td>\n",
       "      <td>-0.02215021</td>\n",
       "      <td>...</td>\n",
       "      <td>0.04540422</td>\n",
       "      <td>-0.01674184</td>\n",
       "      <td>0.04899644</td>\n",
       "      <td>0.00961292</td>\n",
       "      <td>0.13529041</td>\n",
       "      <td>0.00173762</td>\n",
       "      <td>0.13869403</td>\n",
       "      <td>0.04405904</td>\n",
       "      <td>0.03381174</td>\n",
       "      <td>-0.01623981</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 495 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "ticker               A         AAL         AAP        AAPL        ABBV  \\\n",
       "date                                                                     \n",
       "2013-07-31         nan         nan         nan         nan         nan   \n",
       "2013-08-31  0.04181412 -0.18015337 -0.02977582  0.08044762 -0.06518370   \n",
       "2013-09-30  0.09657861  0.15979244  0.03282284 -0.02171531  0.04855545   \n",
       "2013-10-31 -0.00960698  0.14734639  0.18195865  0.09201927  0.08860637   \n",
       "2013-11-30  0.05388057  0.06647111  0.01828314  0.06772063  0.00000000   \n",
       "\n",
       "ticker             ABC         ABT         ACN        ADBE         ADI  ...  \\\n",
       "date                                                                    ...   \n",
       "2013-07-31         nan         nan         nan         nan         nan  ...   \n",
       "2013-08-31 -0.01609335 -0.09440968 -0.02136190 -0.03289558 -0.05749847  ...   \n",
       "2013-09-30  0.07086509 -0.00420927  0.01905603  0.12689741  0.01650096  ...   \n",
       "2013-10-31  0.06693948  0.10058564  0.01124304  0.04296064  0.04671322  ...   \n",
       "2013-11-30  0.07997603  0.04389252  0.05260536  0.04613431 -0.02215021  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2013-07-31         nan         nan         nan         nan         nan   \n",
       "2013-08-31 -0.05879217 -0.06720501 -0.06596571 -0.02097402  0.02845720   \n",
       "2013-09-30  0.04630944  0.07605219 -0.01293321  0.03481157  0.03611367   \n",
       "2013-10-31 -0.00814469 -0.03082169  0.04076620  0.08157415 -0.03460553   \n",
       "2013-11-30  0.04540422 -0.01674184  0.04899644  0.00961292  0.13529041   \n",
       "\n",
       "ticker             XYL         YUM         ZBH        ZION         ZTS  \n",
       "date                                                                    \n",
       "2013-07-31         nan         nan         nan         nan         nan  \n",
       "2013-08-31 -0.00134868 -0.04058203 -0.05402072 -0.05663911 -0.02238899  \n",
       "2013-09-30  0.11966450  0.01937689  0.04028369 -0.01985983  0.06539579  \n",
       "2013-10-31  0.21535825 -0.04870385  0.06287079  0.03494040  0.01922875  \n",
       "2013-11-30  0.00173762  0.13869403  0.04405904  0.03381174 -0.01623981  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 first rows of the monthly_close_returns dataframe to review its information\n",
    "# first date is 2013-07-31\n",
    "# first row in nan because of shift() operation in compute_log_returns() function\n",
    "monthly_close_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>ticker</th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABBV</th>\n",
       "      <th>ABC</th>\n",
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       "      <th>ADI</th>\n",
       "      <th>...</th>\n",
       "      <th>XL</th>\n",
       "      <th>XLNX</th>\n",
       "      <th>XOM</th>\n",
       "      <th>XRAY</th>\n",
       "      <th>XRX</th>\n",
       "      <th>XYL</th>\n",
       "      <th>YUM</th>\n",
       "      <th>ZBH</th>\n",
       "      <th>ZION</th>\n",
       "      <th>ZTS</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-02-28</th>\n",
       "      <td>0.04648289</td>\n",
       "      <td>0.04873915</td>\n",
       "      <td>-0.04757013</td>\n",
       "      <td>0.12552425</td>\n",
       "      <td>0.01187489</td>\n",
       "      <td>0.05135996</td>\n",
       "      <td>0.07626031</td>\n",
       "      <td>0.07305358</td>\n",
       "      <td>0.04281683</td>\n",
       "      <td>0.09464624</td>\n",
       "      <td>...</td>\n",
       "      <td>0.07484917</td>\n",
       "      <td>0.01624776</td>\n",
       "      <td>-0.02195182</td>\n",
       "      <td>0.11358061</td>\n",
       "      <td>0.07101104</td>\n",
       "      <td>-0.02065858</td>\n",
       "      <td>-0.00320978</td>\n",
       "      <td>-0.01061987</td>\n",
       "      <td>0.06402762</td>\n",
       "      <td>-0.03011775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-03-31</th>\n",
       "      <td>0.03263890</td>\n",
       "      <td>-0.09164993</td>\n",
       "      <td>-0.05439459</td>\n",
       "      <td>0.04754147</td>\n",
       "      <td>0.05229538</td>\n",
       "      <td>-0.03344570</td>\n",
       "      <td>-0.01497402</td>\n",
       "      <td>-0.02161979</td>\n",
       "      <td>0.09497211</td>\n",
       "      <td>0.00024408</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.01017620</td>\n",
       "      <td>-0.01593728</td>\n",
       "      <td>0.00844920</td>\n",
       "      <td>-0.01575947</td>\n",
       "      <td>-0.00497178</td>\n",
       "      <td>0.04271546</td>\n",
       "      <td>-0.02197891</td>\n",
       "      <td>0.04404029</td>\n",
       "      <td>-0.06676818</td>\n",
       "      <td>0.00112486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-04-30</th>\n",
       "      <td>0.04040579</td>\n",
       "      <td>0.00753654</td>\n",
       "      <td>-0.04215500</td>\n",
       "      <td>-0.00006961</td>\n",
       "      <td>0.02182202</td>\n",
       "      <td>-0.07567373</td>\n",
       "      <td>-0.01142815</td>\n",
       "      <td>0.02214547</td>\n",
       "      <td>0.02736367</td>\n",
       "      <td>-0.07274784</td>\n",
       "      <td>...</td>\n",
       "      <td>0.04871848</td>\n",
       "      <td>0.08633458</td>\n",
       "      <td>-0.00439937</td>\n",
       "      <td>0.01273092</td>\n",
       "      <td>-0.02064767</td>\n",
       "      <td>0.02341935</td>\n",
       "      <td>0.03320595</td>\n",
       "      <td>-0.02035146</td>\n",
       "      <td>-0.04804045</td>\n",
       "      <td>0.05205758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-31</th>\n",
       "      <td>0.09175337</td>\n",
       "      <td>0.12956238</td>\n",
       "      <td>-0.06173770</td>\n",
       "      <td>0.06557216</td>\n",
       "      <td>0.00121249</td>\n",
       "      <td>0.11615820</td>\n",
       "      <td>0.04524848</td>\n",
       "      <td>0.02579791</td>\n",
       "      <td>0.05894304</td>\n",
       "      <td>0.11819123</td>\n",
       "      <td>...</td>\n",
       "      <td>0.04302745</td>\n",
       "      <td>0.06090411</td>\n",
       "      <td>-0.00482798</td>\n",
       "      <td>0.00441780</td>\n",
       "      <td>-0.01683069</td>\n",
       "      <td>0.01750300</td>\n",
       "      <td>0.09965606</td>\n",
       "      <td>-0.00368417</td>\n",
       "      <td>0.00296435</td>\n",
       "      <td>0.10432630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-30</th>\n",
       "      <td>-0.01497493</td>\n",
       "      <td>0.03869621</td>\n",
       "      <td>-0.13591186</td>\n",
       "      <td>-0.05891588</td>\n",
       "      <td>0.09376676</td>\n",
       "      <td>0.02963180</td>\n",
       "      <td>0.06260663</td>\n",
       "      <td>-0.00636714</td>\n",
       "      <td>-0.00296506</td>\n",
       "      <td>-0.09185947</td>\n",
       "      <td>...</td>\n",
       "      <td>0.00769349</td>\n",
       "      <td>-0.03648424</td>\n",
       "      <td>0.00285307</td>\n",
       "      <td>0.02190798</td>\n",
       "      <td>0.02428615</td>\n",
       "      <td>0.06118855</td>\n",
       "      <td>0.01530084</td>\n",
       "      <td>0.07612942</td>\n",
       "      <td>0.09151416</td>\n",
       "      <td>0.00329757</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 495 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "ticker               A         AAL         AAP        AAPL       ABBV  \\\n",
       "date                                                                    \n",
       "2017-02-28  0.04648289  0.04873915 -0.04757013  0.12552425 0.01187489   \n",
       "2017-03-31  0.03263890 -0.09164993 -0.05439459  0.04754147 0.05229538   \n",
       "2017-04-30  0.04040579  0.00753654 -0.04215500 -0.00006961 0.02182202   \n",
       "2017-05-31  0.09175337  0.12956238 -0.06173770  0.06557216 0.00121249   \n",
       "2017-06-30 -0.01497493  0.03869621 -0.13591186 -0.05891588 0.09376676   \n",
       "\n",
       "ticker             ABC         ABT         ACN        ADBE         ADI  ...  \\\n",
       "date                                                                    ...   \n",
       "2017-02-28  0.05135996  0.07626031  0.07305358  0.04281683  0.09464624  ...   \n",
       "2017-03-31 -0.03344570 -0.01497402 -0.02161979  0.09497211  0.00024408  ...   \n",
       "2017-04-30 -0.07567373 -0.01142815  0.02214547  0.02736367 -0.07274784  ...   \n",
       "2017-05-31  0.11615820  0.04524848  0.02579791  0.05894304  0.11819123  ...   \n",
       "2017-06-30  0.02963180  0.06260663 -0.00636714 -0.00296506 -0.09185947  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2017-02-28  0.07484917  0.01624776 -0.02195182  0.11358061  0.07101104   \n",
       "2017-03-31 -0.01017620 -0.01593728  0.00844920 -0.01575947 -0.00497178   \n",
       "2017-04-30  0.04871848  0.08633458 -0.00439937  0.01273092 -0.02064767   \n",
       "2017-05-31  0.04302745  0.06090411 -0.00482798  0.00441780 -0.01683069   \n",
       "2017-06-30  0.00769349 -0.03648424  0.00285307  0.02190798  0.02428615   \n",
       "\n",
       "ticker             XYL         YUM         ZBH        ZION         ZTS  \n",
       "date                                                                    \n",
       "2017-02-28 -0.02065858 -0.00320978 -0.01061987  0.06402762 -0.03011775  \n",
       "2017-03-31  0.04271546 -0.02197891  0.04404029 -0.06676818  0.00112486  \n",
       "2017-04-30  0.02341935  0.03320595 -0.02035146 -0.04804045  0.05205758  \n",
       "2017-05-31  0.01750300  0.09965606 -0.00368417  0.00296435  0.10432630  \n",
       "2017-06-30  0.06118855  0.01530084  0.07612942  0.09151416  0.00329757  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 last rows of the monthly_close_returns dataframe to review its information\n",
    "# last date is 2017-06-30\n",
    "monthly_close_returns.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shift Returns\n",
    "Implement the `shift_returns` function to shift the log returns to the previous or future returns in the time series. For example, the parameter `shift_n` is 2 and `returns` is the following:\n",
    "\n",
    "```\n",
    "                           Returns\n",
    "               A         B         C         D\n",
    "2013-07-08     0.015     0.082     0.096     0.020     ...\n",
    "2013-07-09     0.037     0.095     0.027     0.063     ...\n",
    "2013-07-10     0.094     0.001     0.093     0.019     ...\n",
    "2013-07-11     0.092     0.057     0.069     0.087     ...\n",
    "...            ...       ...       ...       ...\n",
    "```\n",
    "\n",
    "the output of the `shift_returns` function would be:\n",
    "```\n",
    "                        Shift Returns\n",
    "               A         B         C         D\n",
    "2013-07-08     NaN       NaN       NaN       NaN       ...\n",
    "2013-07-09     NaN       NaN       NaN       NaN       ...\n",
    "2013-07-10     0.015     0.082     0.096     0.020     ...\n",
    "2013-07-11     0.037     0.095     0.027     0.063     ...\n",
    "...            ...       ...       ...       ...\n",
    "```\n",
    "Using the same `returns` data as above, the `shift_returns` function should generate the following with `shift_n` as -2:\n",
    "```\n",
    "                        Shift Returns\n",
    "               A         B         C         D\n",
    "2013-07-08     0.094     0.001     0.093     0.019     ...\n",
    "2013-07-09     0.092     0.057     0.069     0.087     ...\n",
    "...            ...       ...       ...       ...       ...\n",
    "...            ...       ...       ...       ...       ...\n",
    "...            NaN       NaN       NaN       NaN       ...\n",
    "...            NaN       NaN       NaN       NaN       ...\n",
    "```\n",
    "_Note: The \"...\" represents data points we're not showing._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tests Passed\n"
     ]
    }
   ],
   "source": [
    "def shift_returns(returns, shift_n):\n",
    "    \"\"\"\n",
    "    Generate shifted returns\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    returns : DataFrame\n",
    "        Returns for each ticker and date\n",
    "    shift_n : int\n",
    "        Number of periods to move, can be positive or negative\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    shifted_returns : DataFrame\n",
    "        Shifted returns for each ticker and date\n",
    "    \"\"\"\n",
    "    # TODO: Implement Function\n",
    "    # shift() function, moves data returns in a given period shift_n\n",
    "    shifted_returns = returns.shift(shift_n)\n",
    "    # return shifted_returns\n",
    "    return shifted_returns\n",
    "\n",
    "project_tests.test_shift_returns(shift_returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View Data\n",
    "Let's get the previous month's and next month's returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "layout": {
        "title": "Previous Returns of AAPL Stock"
       }
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      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "prev_returns = shift_returns(monthly_close_returns, 1)\n",
    "lookahead_returns = shift_returns(monthly_close_returns, -1)\n",
    "\n",
    "project_helper.plot_shifted_returns(\n",
    "    prev_returns.loc[:, apple_ticker],\n",
    "    monthly_close_returns.loc[:, apple_ticker],\n",
    "    'Previous Returns of {} Stock'.format(apple_ticker))\n",
    "project_helper.plot_shifted_returns(\n",
    "    lookahead_returns.loc[:, apple_ticker],\n",
    "    monthly_close_returns.loc[:, apple_ticker],\n",
    "    'Lookahead Returns of {} Stock'.format(apple_ticker))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate Trading Signal\n",
    "\n",
    "A trading signal is a sequence of trading actions, or results that can be used to take trading actions. A common form is to produce a \"long\" and \"short\" portfolio of stocks on each date (e.g. end of each month, or whatever frequency you desire to trade at). This signal can be interpreted as rebalancing your portfolio on each of those dates, entering long (\"buy\") and short (\"sell\") positions as indicated.\n",
    "\n",
    "Here's a strategy that we will try:\n",
    "> For each month-end observation period, rank the stocks by _previous_ returns, from the highest to the lowest. Select the top performing stocks for the long portfolio, and the bottom performing stocks for the short portfolio.\n",
    "\n",
    "Implement the `get_top_n` function to get the top performing stock for each month. Get the top performing stocks from `prev_returns` by assigning them a value of 1. For all other stocks, give them a value of 0. For example, using the following `prev_returns`:\n",
    "\n",
    "```\n",
    "                                     Previous Returns\n",
    "               A         B         C         D         E         F         G\n",
    "2013-07-08     0.015     0.082     0.096     0.020     0.075     0.043     0.074\n",
    "2013-07-09     0.037     0.095     0.027     0.063     0.024     0.086     0.025\n",
    "...            ...       ...       ...       ...       ...       ...       ...\n",
    "```\n",
    "\n",
    "The function `get_top_n` with `top_n` set to 3 should return the following:\n",
    "```\n",
    "                                     Previous Returns\n",
    "               A         B         C         D         E         F         G\n",
    "2013-07-08     0         1         1         0         1         0         0\n",
    "2013-07-09     0         1         0         1         0         1         0\n",
    "...            ...       ...       ...       ...       ...       ...       ...\n",
    "```\n",
    "*Note: You may have to use Panda's [`DataFrame.iterrows`](https://pandas.pydata.org/pandas-docs/version/0.21/generated/pandas.DataFrame.iterrows.html) with [`Series.nlargest`](https://pandas.pydata.org/pandas-docs/version/0.21/generated/pandas.Series.nlargest.html) in order to implement the function. This is one of those cases where creating a vecorization solution is too difficult.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
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       "      <th>ticker</th>\n",
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       "      <td>nan</td>\n",
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       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
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       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
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       "      <th>2013-09-30</th>\n",
       "      <td>0.04181412</td>\n",
       "      <td>-0.18015337</td>\n",
       "      <td>-0.02977582</td>\n",
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       "      <td>-0.05402072</td>\n",
       "      <td>-0.05663911</td>\n",
       "      <td>-0.02238899</td>\n",
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       "      <th>2013-10-31</th>\n",
       "      <td>0.09657861</td>\n",
       "      <td>0.15979244</td>\n",
       "      <td>0.03282284</td>\n",
       "      <td>-0.02171531</td>\n",
       "      <td>0.04855545</td>\n",
       "      <td>0.07086509</td>\n",
       "      <td>-0.00420927</td>\n",
       "      <td>0.01905603</td>\n",
       "      <td>0.12689741</td>\n",
       "      <td>0.01650096</td>\n",
       "      <td>...</td>\n",
       "      <td>0.04630944</td>\n",
       "      <td>0.07605219</td>\n",
       "      <td>-0.01293321</td>\n",
       "      <td>0.03481157</td>\n",
       "      <td>0.03611367</td>\n",
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       "      <td>-0.01985983</td>\n",
       "      <td>0.06539579</td>\n",
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       "      <th>2013-11-30</th>\n",
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       "      <td>0.03494040</td>\n",
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       "ticker               A         AAL         AAP        AAPL        ABBV  \\\n",
       "date                                                                     \n",
       "2013-07-31         nan         nan         nan         nan         nan   \n",
       "2013-08-31         nan         nan         nan         nan         nan   \n",
       "2013-09-30  0.04181412 -0.18015337 -0.02977582  0.08044762 -0.06518370   \n",
       "2013-10-31  0.09657861  0.15979244  0.03282284 -0.02171531  0.04855545   \n",
       "2013-11-30 -0.00960698  0.14734639  0.18195865  0.09201927  0.08860637   \n",
       "\n",
       "ticker             ABC         ABT         ACN        ADBE         ADI  ...  \\\n",
       "date                                                                    ...   \n",
       "2013-07-31         nan         nan         nan         nan         nan  ...   \n",
       "2013-08-31         nan         nan         nan         nan         nan  ...   \n",
       "2013-09-30 -0.01609335 -0.09440968 -0.02136190 -0.03289558 -0.05749847  ...   \n",
       "2013-10-31  0.07086509 -0.00420927  0.01905603  0.12689741  0.01650096  ...   \n",
       "2013-11-30  0.06693948  0.10058564  0.01124304  0.04296064  0.04671322  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2013-07-31         nan         nan         nan         nan         nan   \n",
       "2013-08-31         nan         nan         nan         nan         nan   \n",
       "2013-09-30 -0.05879217 -0.06720501 -0.06596571 -0.02097402  0.02845720   \n",
       "2013-10-31  0.04630944  0.07605219 -0.01293321  0.03481157  0.03611367   \n",
       "2013-11-30 -0.00814469 -0.03082169  0.04076620  0.08157415 -0.03460553   \n",
       "\n",
       "ticker             XYL         YUM         ZBH        ZION         ZTS  \n",
       "date                                                                    \n",
       "2013-07-31         nan         nan         nan         nan         nan  \n",
       "2013-08-31         nan         nan         nan         nan         nan  \n",
       "2013-09-30 -0.00134868 -0.04058203 -0.05402072 -0.05663911 -0.02238899  \n",
       "2013-10-31  0.11966450  0.01937689  0.04028369 -0.01985983  0.06539579  \n",
       "2013-11-30  0.21535825 -0.04870385  0.06287079  0.03494040  0.01922875  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prev_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tests Passed\n"
     ]
    }
   ],
   "source": [
    "def get_top_n(prev_returns, top_n):\n",
    "    \"\"\"\n",
    "    Select the top performing stocks\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    prev_returns : DataFrame\n",
    "        Previous shifted returns for each ticker and date\n",
    "    top_n : int\n",
    "        The number of top performing stocks to get\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    top_stocks : DataFrame\n",
    "        Top stocks for each ticker and date marked with a 1\n",
    "    \"\"\"\n",
    "    # TODO: Implement Function\n",
    "    # copy prev_returns DataFrame as top_stocks DataFrame\n",
    "    top_stocks = prev_returns.copy()\n",
    "    # set all values in top_stocks DataFrame to 0\n",
    "    top_stocks[:] = 0\n",
    "    # convert values in top_stocks to integer\n",
    "    top_stocks = top_stocks.astype(np.int)\n",
    "    # loop over all the rows using DataFrame.iterrows() function\n",
    "    # index is the date and rows is a Pandas Series\n",
    "    for index, row in prev_returns.iterrows():\n",
    "        # obtain the indices columns list (list of tickers) for the top_n stoks in a date\n",
    "        indices_columns = row.nlargest(top_n).index\n",
    "        # set the values for the date and top_n tickers in top_stocks DataFrame to 1\n",
    "        top_stocks.loc[index][indices_columns]=1\n",
    "    # return top_stocks DataFrame\n",
    "    return top_stocks\n",
    "\n",
    "project_tests.test_get_top_n(get_top_n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View Data\n",
    "We want to get the best performing and worst performing stocks. To get the best performing stocks, we'll use the `get_top_n` function. To get the worst performing stocks, we'll also use the `get_top_n` function. However, we pass in `-1*prev_returns` instead of just `prev_returns`. Multiplying by negative one will flip all the positive returns to negative and negative returns to positive. Thus, it will return the worst performing stocks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 Most Longed Stocks:\n",
      "INCY, AMD, AVGO, NFX, SWKS, NFLX, ILMN, UAL, NVDA, MU\n",
      "10 Most Shorted Stocks:\n",
      "RRC, FCX, CHK, MRO, GPS, WYNN, DVN, FTI, SPLS, TRIP\n"
     ]
    }
   ],
   "source": [
    "top_bottom_n = 50\n",
    "df_long = get_top_n(prev_returns, top_bottom_n)\n",
    "df_short = get_top_n(-1*prev_returns, top_bottom_n)\n",
    "project_helper.print_top(df_long, 'Longed Stocks')\n",
    "project_helper.print_top(df_short, 'Shorted Stocks')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>ticker</th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
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       "      <th>ABC</th>\n",
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       "      <th>XL</th>\n",
       "      <th>XLNX</th>\n",
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       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-07-31</th>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-08-31</th>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-09-30</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2013-10-31</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-11-30</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>...</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "<p>5 rows × 495 columns</p>\n",
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      ],
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       "ticker      A  AAL  AAP  AAPL  ABBV  ABC  ABT  ACN  ADBE  ADI  ...  XL  XLNX  \\\n",
       "date                                                           ...             \n",
       "2013-07-31  0    0    0     0     0    0    0    0     0    0  ...   0     0   \n",
       "2013-08-31  0    0    0     0     0    0    0    0     0    0  ...   0     0   \n",
       "2013-09-30  1    0    0     1     0    0    0    0     0    0  ...   0     0   \n",
       "2013-10-31  0    1    0     0     0    0    0    0     1    0  ...   0     0   \n",
       "2013-11-30  0    1    1     0     0    0    0    0     0    0  ...   0     0   \n",
       "\n",
       "ticker      XOM  XRAY  XRX  XYL  YUM  ZBH  ZION  ZTS  \n",
       "date                                                  \n",
       "2013-07-31    0     0    0    0    0    0     0    0  \n",
       "2013-08-31    0     0    0    0    0    0     0    0  \n",
       "2013-09-30    0     0    0    0    0    0     0    0  \n",
       "2013-10-31    0     0    0    1    0    0     0    0  \n",
       "2013-11-30    0     0    0    1    0    0     0    0  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 first rows of the df_long DataFrame to review its information\n",
    "df_long.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
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       "ticker      A  AAL  AAP  AAPL  ABBV  ABC  ABT  ACN  ADBE  ADI  ...  XL  XLNX  \\\n",
       "date                                                           ...             \n",
       "2013-07-31  0    0    0     0     0    0    0    0     0    0  ...   0     0   \n",
       "2013-08-31  0    0    0     0     0    0    0    0     0    0  ...   0     0   \n",
       "2013-09-30  0    1    0     0     0    0    1    0     0    0  ...   0     0   \n",
       "2013-10-31  0    0    0     1     0    0    0    0     0    0  ...   0     0   \n",
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       "\n",
       "ticker      XOM  XRAY  XRX  XYL  YUM  ZBH  ZION  ZTS  \n",
       "date                                                  \n",
       "2013-07-31    0     0    0    0    0    0     0    0  \n",
       "2013-08-31    0     0    0    0    0    0     0    0  \n",
       "2013-09-30    0     0    0    0    0    0     0    0  \n",
       "2013-10-31    1     0    0    0    0    0     1    0  \n",
       "2013-11-30    0     0    1    0    1    0     0    0  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 first rows of the df_short DataFrame to review its information\n",
    "df_short.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>ticker</th>\n",
       "      <th>A</th>\n",
       "      <th>AAL</th>\n",
       "      <th>AAP</th>\n",
       "      <th>AAPL</th>\n",
       "      <th>ABBV</th>\n",
       "      <th>ABC</th>\n",
       "      <th>ABT</th>\n",
       "      <th>ACN</th>\n",
       "      <th>ADBE</th>\n",
       "      <th>ADI</th>\n",
       "      <th>...</th>\n",
       "      <th>XL</th>\n",
       "      <th>XLNX</th>\n",
       "      <th>XOM</th>\n",
       "      <th>XRAY</th>\n",
       "      <th>XRX</th>\n",
       "      <th>XYL</th>\n",
       "      <th>YUM</th>\n",
       "      <th>ZBH</th>\n",
       "      <th>ZION</th>\n",
       "      <th>ZTS</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-07-31</th>\n",
       "      <td>0.04181412</td>\n",
       "      <td>-0.18015337</td>\n",
       "      <td>-0.02977582</td>\n",
       "      <td>0.08044762</td>\n",
       "      <td>-0.06518370</td>\n",
       "      <td>-0.01609335</td>\n",
       "      <td>-0.09440968</td>\n",
       "      <td>-0.02136190</td>\n",
       "      <td>-0.03289558</td>\n",
       "      <td>-0.05749847</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.05879217</td>\n",
       "      <td>-0.06720501</td>\n",
       "      <td>-0.06596571</td>\n",
       "      <td>-0.02097402</td>\n",
       "      <td>0.02845720</td>\n",
       "      <td>-0.00134868</td>\n",
       "      <td>-0.04058203</td>\n",
       "      <td>-0.05402072</td>\n",
       "      <td>-0.05663911</td>\n",
       "      <td>-0.02238899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-08-31</th>\n",
       "      <td>0.09657861</td>\n",
       "      <td>0.15979244</td>\n",
       "      <td>0.03282284</td>\n",
       "      <td>-0.02171531</td>\n",
       "      <td>0.04855545</td>\n",
       "      <td>0.07086509</td>\n",
       "      <td>-0.00420927</td>\n",
       "      <td>0.01905603</td>\n",
       "      <td>0.12689741</td>\n",
       "      <td>0.01650096</td>\n",
       "      <td>...</td>\n",
       "      <td>0.04630944</td>\n",
       "      <td>0.07605219</td>\n",
       "      <td>-0.01293321</td>\n",
       "      <td>0.03481157</td>\n",
       "      <td>0.03611367</td>\n",
       "      <td>0.11966450</td>\n",
       "      <td>0.01937689</td>\n",
       "      <td>0.04028369</td>\n",
       "      <td>-0.01985983</td>\n",
       "      <td>0.06539579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-09-30</th>\n",
       "      <td>-0.00960698</td>\n",
       "      <td>0.14734639</td>\n",
       "      <td>0.18195865</td>\n",
       "      <td>0.09201927</td>\n",
       "      <td>0.08860637</td>\n",
       "      <td>0.06693948</td>\n",
       "      <td>0.10058564</td>\n",
       "      <td>0.01124304</td>\n",
       "      <td>0.04296064</td>\n",
       "      <td>0.04671322</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.00814469</td>\n",
       "      <td>-0.03082169</td>\n",
       "      <td>0.04076620</td>\n",
       "      <td>0.08157415</td>\n",
       "      <td>-0.03460553</td>\n",
       "      <td>0.21535825</td>\n",
       "      <td>-0.04870385</td>\n",
       "      <td>0.06287079</td>\n",
       "      <td>0.03494040</td>\n",
       "      <td>0.01922875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-10-31</th>\n",
       "      <td>0.05388057</td>\n",
       "      <td>0.06647111</td>\n",
       "      <td>0.01828314</td>\n",
       "      <td>0.06772063</td>\n",
       "      <td>0.00000000</td>\n",
       "      <td>0.07997603</td>\n",
       "      <td>0.04389252</td>\n",
       "      <td>0.05260536</td>\n",
       "      <td>0.04613431</td>\n",
       "      <td>-0.02215021</td>\n",
       "      <td>...</td>\n",
       "      <td>0.04540422</td>\n",
       "      <td>-0.01674184</td>\n",
       "      <td>0.04899644</td>\n",
       "      <td>0.00961292</td>\n",
       "      <td>0.13529041</td>\n",
       "      <td>0.00173762</td>\n",
       "      <td>0.13869403</td>\n",
       "      <td>0.04405904</td>\n",
       "      <td>0.03381174</td>\n",
       "      <td>-0.01623981</td>\n",
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       "    <tr>\n",
       "      <th>2013-11-30</th>\n",
       "      <td>0.06769609</td>\n",
       "      <td>0.07267716</td>\n",
       "      <td>0.09197258</td>\n",
       "      <td>0.00886237</td>\n",
       "      <td>0.08616823</td>\n",
       "      <td>-0.00312412</td>\n",
       "      <td>0.00365918</td>\n",
       "      <td>0.05950782</td>\n",
       "      <td>0.05314171</td>\n",
       "      <td>0.06162558</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.00005037</td>\n",
       "      <td>0.03298584</td>\n",
       "      <td>0.07935125</td>\n",
       "      <td>0.02044076</td>\n",
       "      <td>0.07181852</td>\n",
       "      <td>0.00115674</td>\n",
       "      <td>-0.02700927</td>\n",
       "      <td>0.02143144</td>\n",
       "      <td>0.02125228</td>\n",
       "      <td>0.04825498</td>\n",
       "    </tr>\n",
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       "<p>5 rows × 495 columns</p>\n",
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       "ticker               A         AAL         AAP        AAPL        ABBV  \\\n",
       "date                                                                     \n",
       "2013-07-31  0.04181412 -0.18015337 -0.02977582  0.08044762 -0.06518370   \n",
       "2013-08-31  0.09657861  0.15979244  0.03282284 -0.02171531  0.04855545   \n",
       "2013-09-30 -0.00960698  0.14734639  0.18195865  0.09201927  0.08860637   \n",
       "2013-10-31  0.05388057  0.06647111  0.01828314  0.06772063  0.00000000   \n",
       "2013-11-30  0.06769609  0.07267716  0.09197258  0.00886237  0.08616823   \n",
       "\n",
       "ticker             ABC         ABT         ACN        ADBE         ADI  ...  \\\n",
       "date                                                                    ...   \n",
       "2013-07-31 -0.01609335 -0.09440968 -0.02136190 -0.03289558 -0.05749847  ...   \n",
       "2013-08-31  0.07086509 -0.00420927  0.01905603  0.12689741  0.01650096  ...   \n",
       "2013-09-30  0.06693948  0.10058564  0.01124304  0.04296064  0.04671322  ...   \n",
       "2013-10-31  0.07997603  0.04389252  0.05260536  0.04613431 -0.02215021  ...   \n",
       "2013-11-30 -0.00312412  0.00365918  0.05950782  0.05314171  0.06162558  ...   \n",
       "\n",
       "ticker              XL        XLNX         XOM        XRAY         XRX  \\\n",
       "date                                                                     \n",
       "2013-07-31 -0.05879217 -0.06720501 -0.06596571 -0.02097402  0.02845720   \n",
       "2013-08-31  0.04630944  0.07605219 -0.01293321  0.03481157  0.03611367   \n",
       "2013-09-30 -0.00814469 -0.03082169  0.04076620  0.08157415 -0.03460553   \n",
       "2013-10-31  0.04540422 -0.01674184  0.04899644  0.00961292  0.13529041   \n",
       "2013-11-30 -0.00005037  0.03298584  0.07935125  0.02044076  0.07181852   \n",
       "\n",
       "ticker             XYL         YUM         ZBH        ZION         ZTS  \n",
       "date                                                                    \n",
       "2013-07-31 -0.00134868 -0.04058203 -0.05402072 -0.05663911 -0.02238899  \n",
       "2013-08-31  0.11966450  0.01937689  0.04028369 -0.01985983  0.06539579  \n",
       "2013-09-30  0.21535825 -0.04870385  0.06287079  0.03494040  0.01922875  \n",
       "2013-10-31  0.00173762  0.13869403  0.04405904  0.03381174 -0.01623981  \n",
       "2013-11-30  0.00115674 -0.02700927  0.02143144  0.02125228  0.04825498  \n",
       "\n",
       "[5 rows x 495 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the 5 first rows of the lookahead_returns dataframe to review its information\n",
    "lookahead_returns.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Projected Returns\n",
    "It's now time to check if your trading signal has the potential to become profitable!\n",
    "\n",
    "We'll start by **computing the net returns this portfolio would return**. For simplicity, **we'll assume every stock gets an equal dollar amount of investment**. This makes it easier to compute a portfolio's returns as the simple arithmetic average of the individual stock returns.\n",
    "\n",
    "Implement the `portfolio_returns` function to compute the expected portfolio returns. Using `df_long` to indicate which stocks to long and `df_short` to indicate which stocks to short, calculate the returns using `lookahead_returns`. To help with calculation, we've provided you with `n_stocks` as the number of stocks we're investing in a single period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tests Passed\n"
     ]
    }
   ],
   "source": [
    "def portfolio_returns(df_long, df_short, lookahead_returns, n_stocks):\n",
    "    \"\"\"\n",
    "    Compute expected returns for the portfolio, assuming equal investment in each long/short stock.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    df_long : DataFrame\n",
    "        Top stocks for each ticker and date marked with a 1\n",
    "    df_short : DataFrame\n",
    "        Bottom stocks for each ticker and date marked with a 1\n",
    "    lookahead_returns : DataFrame\n",
    "        Lookahead returns for each ticker and date\n",
    "    n_stocks: int\n",
    "        The number number of stocks chosen for each month\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    portfolio_returns : DataFrame\n",
    "        Expected portfolio returns for each ticker and date\n",
    "    \"\"\"\n",
    "    # TODO: Implement Function\n",
    "    # obtain returns from long positions multiplying df_long by lookahead_returns\n",
    "    long_position_returns = df_long * lookahead_returns\n",
    "    # obtain returns from short positions multiplying df_short by lookahead_returns\n",
    "    short_position_returns = df_short * lookahead_returns\n",
    "    # compute total returns we subtract short_positions_returns \n",
    "    # to long_position_returns because its value is negative\n",
    "    total_returns = long_position_returns - short_position_returns\n",
    "    # compute the average_total_returns\n",
    "    average_returns = total_returns/n_stocks\n",
    "    # return average_returns\n",
    "    return average_returns\n",
    "\n",
    "project_tests.test_portfolio_returns(portfolio_returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View Data\n",
    "Time to see how the portfolio did."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
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       "<div id=\"8a533ad9-6c5b-4d2a-942a-62b7ee75f0cf\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"8a533ad9-6c5b-4d2a-942a-62b7ee75f0cf\", [{\"type\": \"scatter\", \"line\": {\"color\": \"#2D3ECF\"}, \"mode\": \"line\", \"y\": [0.0, 0.0, -0.002364561950000154, -0.0022274399233187516, -0.0009682848595743732, 0.002644290703890742, -0.004869723041469705, -0.007614062918999826, -0.008930449416135376, -0.007255007281348456, -0.00938457402540588, -0.002472281868246124, 0.01026565789870388, 0.017063718128497364, 0.012594151953000999, 0.033621850536666616, 0.012017855737879503, 0.011523131190895052, -0.01759709185116824, 0.022544552969585074, 0.00792112277537717, 0.025396671262614863, -0.012030123217369638, 0.03572642550283469, -0.0030489344184420207, 0.03952277374659436, -0.011829474798826154, 0.012645697917860767, -0.0022217155584035512, -0.019010506000701838, 0.009874804062808334, -0.010678938060237285, -0.025892235227243647, -0.0024255819500312594, -0.0005645897832661938, -0.002552477774413796, -0.032999620666274126, 0.0013687279596140767, 0.009895776024915962, 0.007437763223292415, 0.013181132158052392, -0.010546089504143395, 0.013530612712879203, 0.02290161096760456, 0.010740369231499463, 0.016457276906924768, 0.0014763342897174585, 0.0], \"name\": \"Returns\", \"x\": [\"2013-07-31\", \"2013-08-31\", \"2013-09-30\", \"2013-10-31\", \"2013-11-30\", \"2013-12-31\", \"2014-01-31\", \"2014-02-28\", \"2014-03-31\", \"2014-04-30\", \"2014-05-31\", \"2014-06-30\", \"2014-07-31\", \"2014-08-31\", \"2014-09-30\", \"2014-10-31\", \"2014-11-30\", \"2014-12-31\", \"2015-01-31\", \"2015-02-28\", \"2015-03-31\", \"2015-04-30\", \"2015-05-31\", \"2015-06-30\", \"2015-07-31\", \"2015-08-31\", \"2015-09-30\", \"2015-10-31\", \"2015-11-30\", \"2015-12-31\", \"2016-01-31\", \"2016-02-29\", \"2016-03-31\", \"2016-04-30\", \"2016-05-31\", \"2016-06-30\", \"2016-07-31\", \"2016-08-31\", \"2016-09-30\", \"2016-10-31\", \"2016-11-30\", \"2016-12-31\", \"2017-01-31\", \"2017-02-28\", \"2017-03-31\", \"2017-04-30\", \"2017-05-31\", \"2017-06-30\"]}], {\"title\": \"Portfolio Returns\"}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"displayModeBar\": false})});</script>"
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   ],
   "source": [
    "expected_portfolio_returns = portfolio_returns(df_long, df_short, lookahead_returns, 2*top_bottom_n)\n",
    "project_helper.plot_returns(expected_portfolio_returns.T.sum(), 'Portfolio Returns')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistical Tests\n",
    "### Annualized Rate of Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Mean:                       0.003185\n",
      "Standard Error:             0.002158\n",
      "Annualized Rate of Return:  3.90%\n",
      "\n"
     ]
    }
   ],
   "source": [
    "expected_portfolio_returns_by_date = expected_portfolio_returns.T.sum().dropna()\n",
    "portfolio_ret_mean = expected_portfolio_returns_by_date.mean()\n",
    "portfolio_ret_ste = expected_portfolio_returns_by_date.sem()\n",
    "portfolio_ret_annual_rate = (np.exp(portfolio_ret_mean * 12) - 1) * 100\n",
    "\n",
    "print(\"\"\"\n",
    "Mean:                       {:.6f}\n",
    "Standard Error:             {:.6f}\n",
    "Annualized Rate of Return:  {:.2f}%\n",
    "\"\"\".format(portfolio_ret_mean, portfolio_ret_ste, portfolio_ret_annual_rate))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The annualized rate of return allows you to compare the rate of return from this strategy to other quoted rates of return, which are usually quoted on an annual basis. \n",
    "\n",
    "### T-Test\n",
    "Our null hypothesis ($H_0$) is that the actual mean return from the signal is zero. We'll perform a one-sample, one-sided t-test on the observed mean return, to see if we can reject $H_0$.\n",
    "\n",
    "We'll need to first compute the t-statistic, and then find its corresponding p-value. The p-value will indicate the probability of observing a mean return equally or more extreme than the one we observed if the null hypothesis were true. A small p-value means that the chance of observing the mean we observed under the null hypothesis is small, and thus casts doubt on the null hypothesis. It's good practice to set a desired level of significance or alpha ($\\alpha$) _before_ computing the p-value, and then reject the null hypothesis if $p < \\alpha$.\n",
    "\n",
    "For this project, we'll use $\\alpha = 0.05$, since it's a common value to use.\n",
    "\n",
    "Implement the `analyze_alpha` function to perform a t-test on the sample of portfolio returns. We've imported the `scipy.stats` module for you to perform the t-test.\n",
    "\n",
    "Note: [`scipy.stats.ttest_1samp`](https://docs.scipy.org/doc/scipy-1.0.0/reference/generated/scipy.stats.ttest_1samp.html) performs a two-sided test, so divide the p-value by 2 to get 1-sided p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "date\n",
       "2013-07-31    0.00000000\n",
       "2013-08-31    0.00000000\n",
       "2013-09-30   -0.00236456\n",
       "2013-10-31   -0.00222744\n",
       "2013-11-30   -0.00096828\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show the expected_portfolio_returns_by_date DataFrame\n",
    "expected_portfolio_returns_by_date.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.series.Series"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(expected_portfolio_returns_by_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tests Passed\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "def analyze_alpha(expected_portfolio_returns_by_date):\n",
    "    \"\"\"\n",
    "    Perform a t-test with the null hypothesis being that the expected mean return is zero.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    expected_portfolio_returns_by_date : Pandas Series\n",
    "        Expected portfolio returns for each date\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    t_value\n",
    "        T-statistic from t-test\n",
    "    p_value\n",
    "        Corresponding p-value\n",
    "    \"\"\"\n",
    "    # TODO: Implement Function\n",
    "    # compute the t_value and p_value with the stats.ttest_1samp() function\n",
    "    # entering the sample observations and the expected value in the null hyphotesis=0\n",
    "    t_value, p_value = stats.ttest_1samp(expected_portfolio_returns_by_date,0)\n",
    "    # return t_value, p_value/2\n",
    "    # p_value is divided by 2 because this function returns a two-sided test\n",
    "    return t_value, p_value/2\n",
    "\n",
    "project_tests.test_analyze_alpha(analyze_alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View Data\n",
    "Let's see what values we get with our portfolio. After you run this, make sure to answer the question below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Alpha analysis:\n",
      " t-value:        1.476\n",
      " p-value:        0.073339\n",
      "\n"
     ]
    }
   ],
   "source": [
    "t_value, p_value = analyze_alpha(expected_portfolio_returns_by_date)\n",
    "print(\"\"\"\n",
    "Alpha analysis:\n",
    " t-value:        {:.3f}\n",
    " p-value:        {:.6f}\n",
    "\"\"\".format(t_value, p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: What p-value did you observe? And what does that indicate about your signal?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the t-test, the t-value is 1.467 and **p_value is 0.073359**. \n",
    "\n",
    "Our $\\alpha = 0.05$.\n",
    "\n",
    "For these types of test, we have this two posibilities:\n",
    "\n",
    "- If p $ \\leq \\alpha$: We reject the null hypothesis\n",
    "\n",
    "- If p $ > \\alpha$: We fail to reject the null hypothesis\n",
    "\n",
    "In this analysis, we are in the second case: **the p_value is greater than the desired level of significance** ($\\alpha$), so **WE FAIL TO REJECT THE NULL HYPOTHESIS**, that means we can't reject the Null Hypothesis and **the actual mean return from the signal might be zero**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Submission\n",
    "Now that you're done with the project, it's time to submit it. Click the submit button in the bottom right. One of our reviewers will give you feedback on your project with a pass or not passed grade. You can continue to the next section while you wait for feedback."
   ]
  }
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